SCANNING BEAM RADAR ALTIMETRY FOR LAND SURFACE MONITORING
Sune R. J. Axelsson
Microwave Systems
Saab Missiles AB
S-581 83 Linkoping
Sweden
Commission I
ABSTRACT
The Skylab experiment followed by GEOS-3, Seasat and Geosat clearly showed
the capability of spaceborne radar altimetry for oceanographic
applications such as measurements of wave-height, tidal action and the
deviation from the perfect geoid. Over land areas, however, their use is
highly restricted due
the limi
ground resol
on, the sensitivity to
off-track topography and 1
ations in surface reflectivity. For
that reason, future radar al meters more specifically designed for land
surface monitoring should use narrow-beam antennas with across-scanning
capability. In this paper, the performance of such an instrument is
analyzed in detail. Three types of imagery can be generated by the sensor:
(i) surface topography, (ii) characteristic subpixel roughness height, and
(iii) the radar reflecti
of ground
near-nadir angles of obseron. Main characteri
cs
the timetry
over various types of
land surfaces are discussed.
1
first generation of spaceborne radar al meters, such as Skylab
(1973), GEOS-3 (1975), Seasat (1978) and Geosat (1985) have clearly proved
the capability of the technique for measurements of wave height, tidal
action, and the deviation from the perfect geoid [1J - [5J. Similar kinds
of instruments but with improved performance 11 be carried by ERS-1 and
the Topex
li
[6J, [7J .
All these altimeters were mainly designed for oceanographic applications.
They use a fixed nadir-oriented antenna with a foot-print diameter of
about 20 km. Frequency-modulated pulses are transmitted towards the
sea-surface, and in the receiver, the return waveform is detected after
pulse compression in an array of range cells. The altitude is then
mated from the delay of the leading edge
the pulse return. The
slope of the leading edge is a measure of the significant wave height.
was gradually improved from
range
ution of the above
about 20 m
Skylab, 2 m
and 0.5 m for Seasat, which gives a
precision at altitude measurements over oceans from 1 m for Skylab to
about 5 cm precision for Seasat.
1. . 1
the leading edge of the pulse
in an area close to the nadir
return are ilt up
response is
di
on .
from more
in the nadir
leading edge
When
di
on
is reduced
ghly depends upon
height of 4 m, for
is about 2 km (
1)
e
hei ght
resol
on becomes too poor for most applications, however. Contrary to
oceanographic profiling, the leading edge of
return pulse is more
affected by offtopography and strong local variations in surface
refl ecti vi ty .
Consequently, the ground resolution of future al metry systems more
specifically dedicated to ice- and land-surface mapping, should be
radically improved. The
mate aim would be a spatial resolution of
estimation of less than one
about 200x200 m and an error at the alti
metre. In order to
ieve annual mapping of the globe, the swath-width
should exceed 6 km.
an Advanced Scanning
2
2.1
Principles of operation
The above requireme
more advanced radar
scanned across
on mapping capability might be satisfied by using a
meter th a very narrow antenna beam, which is
1i
sides improved topographic
roughness information, this
sensor also provides highution maps of the surface reflecti ty
close to the nadir direction, which often contains a signi cant amount of
near-specular returns. The imagery will
a useful complement to
onal SAR-data from more oblique angles
observation.
By introduci
on
as well.
mul ple doppler beams in the forward direction each
can be
at
es
i dence
in N range cells reprein a similar way as for the
1. . 1
From the range cell samples (
mated usi
element can be
),
mean range to the resolution
rJ
R :::
(2.1 )
where
N
::::
L
(2 .. 2 )
is
of
a
measure
refl
, Ao is
resolution element (0°).
i
For estimations
cell, the range
resol
by
1
(rms)
on
(2 .. 3 )
The third and
orders of
(2 .. 4 )
::::
might also be
shape, such as
cs of the pulse
pulse shape,
1 information
For more detailed analyses
content of the range cells {Ak' Rk } might be necessary.
2
Antenna size
The requirement
a
on
m calls for
very large antenna dimensions across-track . In the forward direction, the
extent can be reduced, however, because narrow beams are easily generated
using dopplerbeam sharpening or synthetic aperture technique.
At the carrier frequency 35
and the orbit altitude 800 km, an antenna
1ength of 40 m is required across-track in order to achieve a ground
on
resol
me For an
space shuttle
(H : : : 240
across
12 m,
however .
Further size reductions are
(H : : : 800 km) and 4.5 m (H : :
increased
necessary
ble in the
GHz-band, gi ng L : : : 15 m
km), respectively. A disadvantage is the
at higher frequencies, which will make it
c
pulse-delay.
I ... 1
2
on
d
H
=
A.
near-
2 5)
r
e minimum
on
ons.
me
on is:
1
1;
:::::
-=
.6)
2
In order
nuous
d
scan
me
(2.7)
dN
=
i
on .
d
w=
in
on
(2.8 )
=
1;
er
If H = 240 km,
7 km . For N = 30
To
t
ble
>
If d =
m,
A. = 0 .. 01
H
in a
wi
its
5) Lld
:::
EO
:::
( m+O .. 5) Lld
(3.1)
,..,....,.. . . "" . . of the antenna
on
P(n,
(n
nt area.
is
from
(3.2)
:::
where Ps is transmitted power, A is the electromagnetic wavelength, Lp
represents atmospheric
system losses in the
ver, and
G(n,m) is
rection of
ution el
(n,m) .
a
If
a
is
R(n m)
:::
<I>(n,
::::
r(n
::::
1
)(
[(
us
(3.3)
(3.4)
2)1
(X n
)cos<l>]1
on.
a
1... 1
/
--
y
SWATH-WIDTH
Figure 1. Definition of geometry.
By using the fact that h « Ro and
(3.3) can be applied:
~
« 1, the following approximation of
R(n,m) = Ho-h(n,m}+(Xn2+Ym2}/(2He}
(3.5)
in which:
(3.6)
The broadening effect of the pulse width can be taken into account by a
convolution of the impulse function return from the ground with:
1
x2)
exp(- /2;a
p(x)
= --
(3.7)
2;
where
c
(J
= '2 1"p
(3 . 8)
and 1"p represents the root-mean-square width of the transmitted pulse.
An alternative more simplified method is to add a Gaussian range noise
component to eqn. (3.3) or (3.5) with zero mean and variance according to
eqn. (3 . 8).
1... 1
3.2
Single-pulse response
Equations (3.1) - (3.6) define the range and power received from a
reflector located at (Xn,Y m) and h{n,m) above the reference surface. Each
range bin of the receiver aefines a range interval RK ± 6Rb' where lRb is
half the range resolution.
Let us now subdivide the grid into subsets SK with K = 1 to Nb
corresponding to the different range bins in such a way that SK will
represent 1 reflectors (n,m) on ground satisfying RK-6Rb<R{n,m)<RK+6Rbo
Hence:
(3 . 9)
The amplitude of the pulse return in the K-th range bin is then estimated
from:
(3 .. 10)
where
UK = ~ 12P(n,m)' cos[a(n,m) ]
SK
VK = ~ 12P(n,m)' sin[a(n,m) ]
SK
(3.11)
and
4-n;
a(n,m) = -A.
R(n,m)+~(n,m)
(3.l2)
Over a rough, incoherently scattering surface, a(n,m) is uniformly
distributed (0,2-n;). If no reflector gives a dominating response, UK and VK
are Gaussian and statistically independent with zero means. As a result,
AK becomes Rayleigh-distributed with the probability density function:
AK
AK2
(3.13)
P(AK) = - exp (- - )
PK
2P K
where PK is the total received power in the K-th range bin:
(3.14)
PK = ~ P(n,m)
SK
The relationships (3.10) and (3.13) presume a linear envelope detector.
For a s~uar~-law detector, the envelope of the pulse return is given by
BK = UK +VK and eqn. (3.13) is replaced by an exponential distribution.
1. . 1 1
se
3
a result of the pulse-to-pulse variations of a(n,m) in eqn.
.11) the
envelope samples AK are fading. The mean pulse response is obtained by
averaging eqn. (3 . 10) with a uni
distributed (0,2 TI ) .. For a nonspecular surface wi
Rayle;
(linear detector):
(3 . 15)
a
3
Usually,
analysis
number
(N )
p
1
where AKn is the envelope
(3 . 16)
the n-
pulse return in the K-th range
n.
surfaces with a low amount
coherent scattering, the correlation
between neighbouring pulses can usually be neglected, if pulse-limited
altimeters, such as Seasat or ERS-1, are used8 For a beam-limited
altimeter with d = 200 m, H = 800 km, ~ = 0.01 m and v = 8000 mis, the
doppler bandwidth is only 400
,whi
means a high correlation between
adjacent
ses
pulse
on
es exceedi
1000
4
4.1
s . (2 . 2)
(2.3),
d
se i
average range to the reflectors inside the resolution cell, while the
pulse width is a measure of the range spread or the local surface
roughness.
1-1
Over homogeneous surfaces, the statistics of the fading envelope according
to (3.13) - (3.14) gives a main contribution to the estimation errors of
mean range and rms range spread. The influence of fading is minimized by
smoothing several statistically independent pulse envelopes. A smoothing
effect at the estimation of Rand aR is also obtained, when the range
spread (aR) is much larger than the range resolution (~R) of the
al timeter.
4
I nnc~mo~~eneOlJS
on
15
For inhomogeneous surfaces, variations in surface reflectance can give
significant errors. Let us as an example consider the case, when the pulse
response originates from two surfaces with different reflectance (al ° and
a20) and located at the distances Rl and R2 = R1+O, respectively, from the
altimeter. If the two surfaces cover the portions PI and P2 = (1-Pl) of
true average range (R) and rms range spread (a)
the foot-print area,
are
R
=
P2 R2 = Rl + (I-P1)0
r==~
(4 .. 1 )
=VP l (I- P1)0
If we negl
the fading effect, the weighted average range and rms value
measured by the altimeter are given by a formally similar expression
rJ
R = R1 + (1- P)0
(4 .. 2 )
aR =vp( 1-p)0
but
th the weighting factor redefined as
p = a1 °Pl/(a1 °P1 + (1- P1)a2°)
(4 . 3)
Hence, (4.1) and (4.2) agree, only if a1 ° = 02°. The relationships
(4.2)-(4.3) also mean that ground surface elements with strong reflectance
are given an increased importance at the averaging procedure.
If P = 0.5 and a1°
while
R= R1
aR
= 0.1a2°,
for instance, R = R1+0 . 50 and a
= 0.50,
+ 0.90
= 0 . 30
are predicted from the received pulse waveform.
Consequently, significant errors are generated, when the altimeter beam
crosses the boundary between two fferent kinds of surfaces. An extreme
case is when the altimeter beam passes from sea in over an elevated land
plateau. Oue to the much higher back-scattering from the water, the altimeter measures the range to the water surface until almost the complete
sensitivity beam is taken up by land surface reflectors. As a result the
detected shore-line profile is displaced half a resolution element.
1-1
Similar types of errors are obtained over~volume scattering mediums such
as forests. The detected centroid range (R) and range spread (0R) are then
highly influenced by the scattering characteristics of the ground surface
and the tree elements. Some a priori knowledge of the scattering behaviour
will improve the accuracy at estimations of significant tree height or
tree density, based upon a or a more detailed pulse shape analysis.
Predicted pulse responses ~rom forests are shown in Figure 3 assuming
homogeneous reflectance.
Sloping effects
4.3
In general, the accuracy of the altimetry measurements will be reduced, if
the surface element is not perpendicular to the sensitivity beam . This
means that some degradation is obtained for sloping surface elements~ or
resolution cells which are far away from the subsatellite point.
Let us analyse this behaviour for homogeneous surface elements. If fading
effects are neglected, we can approximately express the normalized beam
function as follows:
where x = y = 0 is the subsatellite point, (xo'Yo) defines the centre of
the resolution element on ground, and 0X' 0y are the rms widths of the
resolution element along-track and across-track, respectively.
According to Eqs. (3.5), the range to a reflector on the ground located
h(x,y) above a spherical reference surface can be described by
(4 .. 4 )
Let us describe the local variations of h(x,y) within the surface element
at (xo'Yo) as
(4.5 )
where ho is the weighted mean deviation from the reference surface, and a,
bare tne local mean surface slopes in x- and y-directions. The deviation
between the real surface topography and the sloping plane surface
approximation is defined by ~(x,y).
The first and second moments of the impulse response from the antenna
foot-print area can be derived from:
R= ffg{x,y)R(x,y)dxdy
r.J
R2 = ffg(x,y)R 2 (x,y)dxdy
(4.6)
,-v
where R corresponds to the centroid of the pulse return.
The rms width of the return pulse is thus:
o
=
(4 . 7)
1-164
Substitution of (4.4) - (4.5) into (4.6) yields after simplifications
(4.8 )
The equation means that the measured elevation (h) of a resolution cell at
(xo'Yo) has a negative bias error given by
(4.9)
As an example, a bias of 0.6 m is obtained for He : 800 km, Xo = 0 and
Yo : 1 km. For Yo = 4 km, ~ is increased to 10 m. This error can be
corrected, however, since xo' Yo' Ox and 0y are supposed to be known.
From (4.9), an uncertainty in xo' Yo will give the following error after
bias correction
(4.10)
For H : 800 km, Xo : 0, Yo : 4 km and AYo : 100 m, an elevation error of
~h : 0.5 m is obtalned. For a swath width of 20 km (YoMaX = 10 km) the
error is increased to 1.2 m. At low orbit measurements from the space
shuttle (240 km), the bias is increased a 3.3 factor.
Sloping terrain and off-nadir observations have also a significant
effect upon the detected pulse width. From (4.4) - (4.8), the rms range
spread (oR) is given by
oR 2 =
2
0T) +0X
2{a-xo/H )2 +0y2 (b-yo/H )2
e
e
(4.11)
where
0
T)
2
r-'
(4.12)
:T)2_rL
T)
is the local surface roughness height (rms) that would be measured at
nadir observations over a horizontal surface (a : b : Xo = Yo: 0).
From (4.11), we find for Ho : 800 km and ° : a : 100 m (i.e. a
resolution element of 200 x 200 m) that a flat ~orizontal surface element
gives OR : 1.2 m, when the sensitivity is pointing 10 km off-track.
If Ho : 240 km, oR is increased to 4 m.
For non-horizontal surface elements, the pulse response is further
widened. If a : a and b : 0.03 (i.e. two degrees inclination), oR : 3 m is
ob~ained for Ho : 800 km and resolution elements close to the sUDsatellite
pOlnt (x o : Yo : 0).
Even in that case, however, the increased roughness response from groups
of trees should be detectable using the oR-value.
If the topographic variations have a correlation length larger than the
resolution element, most of the sloping effect can be compensated by using
R-estimates of adjacent resolution cells.
1... 165
Over flat areas such as a water surface or sea-ice, the sloping surface
effects can usually be neglected (a = b = 0).
range spread
ation
with scanning angle (
) in (4.11) can then be compensated for, which
improves
sensi
mon;
ng areas wi
ice- dges, for
instance. Examples
cted pulse responses from sea-ice are
in
Fi gure 4.
5
CONCLUSIONS
design and performance of an Advanced Scanning Radar timeter (ASRA)
for high-resolution topographic mapping have been analysed and discussed.
This type of sensor also provides information about the significant
surface roughness height and
scatteri
ent of
resolution cell.
A di
t poi
impl
on
an instrument is
1
antenna aperture required to get a sufficiently narrow beam. By usi
a
GHz) than in earlier ti
higher carrier frequency (35 or
applications and doppler beam sharpening technique in the along-track
direction, the antenna can be reduced to a more convenient size.
The analysis also shows upon a growing altitude bias, when the off-nadir
angle is increased. This effect restri
usable swath-width
high-precision profiling.
The accuracy of surface roughness height estimations based upon the pulse
width will also be signi cantly reduced over hilly ground and over
non-homogeneous areas th great backscattering variations.
ACKNOWLEDGEMENTS
Parts of this research were
out
Linkopi
Uni
ty
financial support from the Swedish Board for Space Activities. I am also
grateful to lng-Marie Pilemalm for typing this manuscript.
REFERENCES
[1 ]
Dooley, R.P. and Brooks, L.W., 1974. Radar altimetry and ocean
wave height estimation. Technology Service Corporation,
Maryland, Contract NAS6-2241.
[2 ]
McGoogan, J.T., Miller, L.S., Brown, G.S. and Hayne, G.S., 1974.
The S-193 Radar altimeter experiment. Proc. IEEE, 62 (6):
793-803.
[3 ]
Townsend, W.F., 1980. An initial assessment of the performance
achieved by the Seasat-1 Radar Altimeter, IEEE J. Oceanic
:2, pp 80-92.
Engin., vol.
1. . 1
[4 ]
, G.H.,
, DeB.,
oceanographic satellite
• 8, pp 16.
[5 ]
1
ssion. J
7.
[6 ]
• A
ons J •
ins
cal Di
, C.G.
radar
uses of
[7 ]
[8 ]
Axelsson,
from rough
SEA-STATE MONITORING
SWH= 0 M •••.•••
SWH= 2.0 M---
SWH=4 M
.
o
'If"
o
o
o~---~~--~----~~-r~~~~~~--r----+
eL25
-20
-is
-to
-5
o
5
15
RANGE DEVIATION (M)
se responses from a seaOx ::: 0y ::: 100 m, Ho ::: 800 km,
1-1
versus
::: 0,
0
~...
w
0
::::>
5
Q.,
w
0
::::>
TREE DENSITY OF 80%
5
MAXIMUM TREE HEIGHT OF
«
~
-
::E
::E
«
0
0
w
N
::;
...~
«
::E
w
N
::;
« ~
H=10 M
::E
IX:
IX:
H=20 M
0
Z
MAXIMUM TREE HEIGHT OF 20 M
AND VARIABLE TREE DENSITY
Q.,
1000/0
0
z
II
~
0
.{
!., ....................: . .....:. . . ......... :::
~:~
~
0
I
I
I
,..,. .... , ......... ,',.,.J
0
0
<e;
<e;
0
0
~+---~--~--.---.---~--.---.---+
-20
fO
15
-is -fO
S
-s
0..25
~+---r-~.-~----~----~--~----~--+
-20
-is -40
-s
f5
"
5
U3
0..25
RANGE DEVIATION (M)
RANGE DEVIATION (M)
Figure 3. Predicted average pulse returns from a flat land area covered
by wood, showing how the tree height (h o) influences the pulse-width and
the tree density (p) the plateau amplitude of the tree response.
Homogeneous reflectance, uniformly distributed tree reflectors with height
(0, ho)' ~R = 0.5 m, Ox = 0y = 100 m, and Xo = Yo = a were assumed.
W
~...
I
I
I
I
0
::::>
::;
MAXIMUM RIDGE HEIGHT
I-
I
I
~+-__~I__~I__~I____~I__~I__~J____~I____-+
I
W
PULSE RESPONSE VERSUS
0
5
::E
Q.,
«
::E
«
0
w
N
::;
«
PULSE RESPONSE VERSUS RIDGE DENSITY
Q.,
MAXIMUM RIDGE HEIGHT: 3.0 M
0
w
...~
RIDGE COVER:
50%
~
r-
«
::E
::E
IX:
0
IX:
z
0
z
·······0.0 M
0
~-
---- 1.0 M
0
I
I
I
3.0
o
<e;-
o
r'"
5.0 M
i
i
i
i
I
I
..I:I'
I:
I
I
I
I
I .
rl
I:
,:
I:
.:
20%
'i
i
8'+---~I--~I--~I--~I~~I~~I--~I---+
i J ';
0..25
-20
-t5
-to
-s
0
5
to
~+---~I--~I----~I----~I~j--'I~~I----~I---+
0..25
-20
-15
-iO
-S
0
5
to
15
t5
RANGE DEVIATION (M)
RANGE DEVIATION (M)
Figure 4. Predicted average pulse returns from rough sea-ice with ridges
showing the influence of height and density upon the pulse shape.
1... 1